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Freeness over the diagonal for large random matrices
journal contribution
posted on 2023-06-07, 06:59 authored by Benson Au, Guillaume Cébron, Antoine DahlqvistAntoine Dahlqvist, Franck Gabriel, Camille MaleWe prove that independent families of permutation invariant random matrices are asymptotically free with amalgamation over the diagonal, both in expectation and in probability, under a uniform boundedness assumption on the operator norm. We can relax the operator norm assumption to an estimate on sums associated to graphs of matrices, further extending the range of applications (e.g., to Wigner matrices with exploding moments and the sparse regime of the Erdos–Rényi model). The result still holds even if the matrices are multiplied entrywise by random variables satisfying a certain growth condition (e.g., as in the case of matrices with a variance profile and percolation models). Our analysis relies on a modified method of moments based on graph observables.
History
Publication status
- Published
File Version
- Accepted version
Journal
Annals of ProbabilityISSN
0091-1798Publisher
Institute of Mathematical StatisticsExternal DOI
Issue
1Volume
49Page range
157-179Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Probability and Statistics Research Group Publications
Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2020-05-12First Open Access (FOA) Date
2021-03-19First Compliant Deposit (FCD) Date
2020-05-11Usage metrics
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